I believe that the apostolic gift brings to the church a strong sense of the heavenly and supernatural realm, and of our kingdom mandate and mission to bring heaven to earth. It carries a strong sense of the presence and power of God. As I have indicated, I believe that it is possible for a number of people to have a measure of this gift in the church, but that there are some who are called to be apostles.
As such they not only have a sense of heaven's agenda but they have an awareness of heavenly strategy to achieve the mission. They are people of revelation and strategy - they are both stewards and administrators of the gospel (Eph.3:5,9). They are pioneers, not just in the sense of planting churches (a common misconception), but in terms of breaking open territory (geographical, cultural, situational, relational) for a culture of heaven to come in, and only in this sense are they 'first' (1 Cor.12:28) and not in terms of hierarchy or rank. In relation to the church, they are architects (1 Cor.3:10) - visionaries and strategists - and fathers (1 Cor.4:15) - drawing churches and/or ministries together, influencing the culture of church/teams and passing on an inheritance of revelation to others (I have come to see fatherhood as key to understanding the role of apostles). Together with prophets, they bring stability and strength to God's house; they are foundations (Eph.2:20)
As such they will have a charismatic authority according to their grace gifting, but it does not require them to have a governmental authority to every church they influence. Even when they do contribute to the government of a local church, it is (as a father to the family) in a relational context and with an empowering spirit, and the nature of how it is exercised changes as the church grows and local leadership becomes more established. Indeed, because all apostles have something to add to the body - all are ours (1 Cor.3:21-22) - a church may well draw upon a number of them, though I feel it is likely there will be a primary one and who that is may change at different stages of the church's journey (1 Cor.3:5-6). I am suggesting this as an outline of a possible pattern which I feel does not violate principles.